Question 27 of 31intermediate⚖️ EvaluateShort Answer2 marks

Deepak claims, "There are some multiples of 11 which, when doubled, are still multiples of 11. But other multiples of 11 don't remain multiples of 11 when doubled". Examine if his conjecture is true; explain your conclusion.

Correct Answer

Claim: Deepak says some multiples of 11, when doubled, remain multiples of 11, but others don't.

Analysis: Let n be a multiple of 11. Then n = 11k for some integer k. When doubled: 2n = 2×112 \times 11k = 11 × (2k) 2n is still a multiple of 11.

Conclusion: ∴ ALL multiples of 11, when doubled, remain multiples of 11. Deepak's claim is false.

Exercise: Figure it Out (Section 4) | Q: 11 | (Page Page 22)
For More Understanding

Explanation

The chapter uses algebraic reasoning to analyze divisibility claims. If n is divisible by 11, then n = 11k for some integer k. Doubling gives 2n = 22k = 11(2k), which is clearly divisible by 11. There are no exceptions to this rule.

Solution Steps

  1. Let n be a multiple of 11

  2. n = 11k for some integer k

  3. When doubled: 2n = 2×112 \times 11k = 11 × (2k)

  4. 2n is still a multiple of 11

  5. This holds for ALL multiples of 11

  6. Deepak's claim is false

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